Section: Application Domains
Modeling Biological Systems
Realistic, precise simulation of cell behavior requires detailed, precise models and fine-grain interpretation. At the same time, it is necessary that this simulation be computationally tractable. Furthermore, the models must be comprehensible to the biologist, and claims about properties of the model must be expressed at an appropriate level of abstraction. Reaching an effective compromise between these conflicting goals requires that these systems be hierarchically composed, that the overall semantics provide means for combining components expressed in different quantitative or discrete formalisms, and that the simulation admit stochastic behavior and evaluation at multiple time scales.
In general, numerical modeling of biological systems follows the process shown below.
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Starting from experimental data, sort possible molecular processes and retain the most plausible.
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Build a schema depicting the overall model and refine it until it is composed of elementary steps.
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Translate these steps into mathematical expressions using the laws of physics and chemistry.
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Translate these expressions into time-dependent differential equations quantifying the changes in the model.
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Analyze the differential system to assess the model.
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Elaborate predictions based on a more detailed study of the differential system.
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Test some selected predictions in vitro or in vivo .
This approach has proven substantial properties of various biological processes, as for example in the case of cell cycle [59] . However, it remains tedious and implies a number of limitations that we shortly describe in this section.
Many biochemical processes can be modeled using continuous domains by employing various kinetics based on the mass action law. However quite a number of biological processes involve small scale units and their dynamics can not be approximated using a global approach and needs to be considered unit-wise.
Some of the biological systems are now known to have a switch-like behavior and can only be specified in a continuous realm by using zero-order ultra-sensitive parametric functions converging to a sharply sigmoid function, which artificially complexifies the system.
The lack of formalized translations between each step makes the whole modeling process error-prone, since immersing the high-level comprehensible cartoon into a low-level differential formalism is completely dependent on the knowledge of the modeler and his/her mathematical skills. Maybe even worse, it blurs the explanatory power of the schema.
As an illustration of the last point it is well-known that the same high level process of the lysis/lysogeny decision in lambda bacteriophage infecting an E. coli cell can be specified using different low-level formalisms, each producing unique results contradicting the others.
The assessment step of the modeling process is usually conducted by slow and painful parameter tinkering , upon which some artificial integrators and rate constants are added to fit the model to the experimental data without any clue as to what meanings these integrators could have biologically speaking.
Two complementary approaches are necessary for model validation. The first is the validation from the computer science point of view, and is mainly based on intrinsic criteria. The second is the external validation, and in our case requires confirmation of model predictions by biological experiments.
In addition to classic measures such as indexes of cluster validity, our use of instrinsic criteria in comparative genomics depends on treatment of the organism as a system. We define coherency rules for predictions that take into account essential genes, requirements for connectivity in biochemical pathways, and, in the case of genome rearrangements, biological rules for genome construction. These rules are defined at appropriate levels in each application.
Experimental validation is made possible by collaboration with partner laboratories in the biological sciences.
